hmwk9new - ISyE 3232 Stochastic Manufacturing and Service...

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Unformatted text preview: ISyE 3232 Stochastic Manufacturing and Service Systems Spring 2011 H. Ayhan & J. Dai Homework 9 March 16, 2011 (Due: at the start of class on Thursday, March 31st) 1. A Markov chain is said to be doubly stochastic if both the rows and columns of the transition matrix sum to 1. Assume that the state space is { 1 ,...,N } , and that the Markov chain is doubly stochastic and irreducible. Determine the stationary distribution . (Hint: there are two approaches. One is to solve = P and N i =1 i = 1 in general for doubly stochastic matrices. The other is to first solve a few examples, then make an educated guess about , and finally show that your guess is correct.) 2. Daily demand for paint brushes at a particular store follows the demand distribution: d 1 2 3 4 P ( D = d ) . 5 . 15 . 3 . 04 . 01 . The stock level is reviewed every evening and when warranted an order is placed at the central ware- house to augment stock. Orders arrive over night and are available to meet the demand on the morninghouse to augment stock....
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